If f and g are two uniformly continuous functions, I need to show that their product is also uniformly continuous. I started with the definition of uniform continuity but got nowhere...
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You're not going to get anywhere, either, unless you restrict the domain. Is uniformly continuous on ? What about ?
Sorry I'm not sure what you mean by that...
Let be given by . Is f uniformly continuous? What about the product of f with f?
yea I haven't figured it out yet... it's probably simple but i'm having a lot of trouble with this one
is trivially uniformly continuous since so the product is not uniformly continuous, namely is not uniformly continuous.
lol but this is isn't making sense since I'm supposed to show the product IS uniformly continuous
IT'S NOT TRUE, and i've provided a counterexample.
lol you're right, now what if both functions were bounded?
Originally Posted by CrazyCat87 yea I haven't figured it out yet... it's probably simple but i'm having a lot of trouble with this one I accept with information: is trivially uniformly continuous since
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